Help on conservation energy

A brass spring (with spring constant k) with no mass on it hangs vertically from fixed support bar, at rest. You attach a mass m to the free end and release it; how far does the mass drop before the spring brings it to a (brief) stop and it starts to bounce back: Use conservation of energy, and show your work. Solve for your answer in terms of k, m, and g. Ignore mass of the spring itself.

2) Your spring stretches more than 50 cm from its rest position, it will become permanently bent out of shape. What is the largest mass ( to 2 significant figures) that you would dare to use for your dropping experiment in part (a)? Assume the same value for k.

I'm going to have to venture a guess at this, since you haven't posted any of your work.

You need to establish a baseline for the potential energy. It doesn't matter where it is because only the change in potential energy is what's important, but you need to arbitrarily establish one never-the-less. I suggest using either the rest position of the spring or the (as yet unknown) lowest position of the mass.

From there, why don't you write the conservation of energy equation and see what you get?

Observe that the kinetic energy of the mass at a distance [tex]x[/tex] from rest equals the energy transferred by gravity ( [tex]mgx[/tex] ) minus the energy absorbed by the spring ( [tex]\frac{1}{2}kx^2 [/tex]). Use this info to solve for x when the kinetic energy is zero.

You can verify that result by setting up an equation for the acceleration ( [tex]g-(\frac{k}{m})x[/tex] ) and integrating it to find its velocity and setting that to zero.